1. Field of the Invention
The present invention generally concerns magnetic resonance tomography (MRT) as employed in medicine for examination of patients. The present invention in particular concerns an improved image reconstruction method with regard to the image generation from raw data that have been acquired with a known technique called the propeller technique.
2. Description of the Prior Art
The propeller technique represents a radial scanning method in MRT imaging and is briefly described in the following. A detailed representation is found in “Magnetic Resonance in Medicine 42: 963-969” (1999) by James G Pipe. In the propeller technique, the scanning of k-space ensues on the basis of a series of blades. Each of the blades is composed of L equidistant, parallel phase encoding lines. A blade is composed of the L lines of a conventional k-space trajectory with Cartesian sampling for which the phase coding gradient has the smallest amplitude. The k-space sampling according to the propeller technique proceeds by the individual blades of the series being rotated relative to one another around the center of k-space. The rotation angle o1 and the number N of the total number of blades thereby represent characteristic parameters that are selected such that the series covers or overlaps the entire k-space of interest (see FIG. 2). In comparison with other acquisition techniques in MRT, the propeller technique has the advantage that a circular region (with diameter L) in the center of the k-space is, as it were, covered by each individual blade. The comparison of two different blades with regard to this center data allows movements of the patient to be determined that occur between the acquisition of two blades. This movement information then can be taken into account in the propeller image reconstruction using all measured raw data, so that it is possible to acquire nearly movement-free images (see FIG. 4).
Given a conventional Cartesian scanning in MRT, the measured values (frequency raw data) represent Cartesian grid points. The grid points arranged in a Cartesian manner in the frequency domain enable images to be reconstructed in a simple manner, namely using a simple fast Fourier transformation (FFT). This is not possible in the propeller technique. The propeller technique belongs to the group of non-Cartesian imaging methods (scanning methods) that require a much more complex raw data processing in order to be able to ultimately reconstruct real images from the measured raw data. Image reconstruction methods for the propeller technique according to the prior art are described in the following section.
The current best known image re construction method that can generally be used given non-Cartesian k-space sampling is based on two different procedures:
a) The first method is the “direct Fourier transformation method”. A detailed representation of this method is found in an article of the periodical “IEEE Trans Med Imaging 7: 26-31 (1988) by A. Maeda et al.” This method is very precise, but is not used in practice due to the large processing (calculating) requirement. In this method, the two-dimensional image I(x,y) is reconstructed according to the formula:
      I    ⁡          (              x        ,        y            )        =            ∑              i        =        0                    N                                                  ⁢          s                      ⁢                  w        ⁡                  (          i          )                    ·              s        ⁡                  (                                                    k                x                            ⁡                              (                i                )                                      ,                                          k                y                            ⁡                              (                i                )                                              )                    ·              ⅇ                              j2π            ⁡                          (                                                                    xk                    x                                    ⁡                                      (                    i                    )                                                  +                                                      yk                    y                                    ⁡                                      (                    i                    )                                                              )                                /                      N            S                              wherein (kx(i), ky(i)) represent the k-space coordinates of the measurement point i along the trajectory. s(kx(i)ky(i)) is the measurement result, thus the resonance signal. The weighting function w(i) is necessary in order to generally allow for the non-uniform k-space sampling and the resulting different sampling density in the individually considered k-space points, given non-Cartesian k-space sampling. The summation extends over all Ns measured data packets in the frequency domain.
b) The second method represents is known as the “gridding method”. A detailed explanation of this method is found in an article of the periodical “IEEE Trans Med Imaging 10: 473-478 (1991) by Jackson J I et al.” In a procedure according to the gridding method, each data point, or the data point compensated/corrected by weighting, is subjected to a folding and projected onto a suitable Cartesian grid. This existing raw data set (now Cartesian) is then transformed into the image domain by means of a fast Fourier transformation (FFT). The desired image can be obtained in that the result of this FFT is divided by the Fourier-transformed kernel core (inverse folding, or deconvolution).
All presently-publicized image reconstruction methods use the gridding method with regard to the propeller technique. Aside from these two techniques a) and b) that are both applicable to k-space samples along arbitrary k-space trajectories, still further image reconstruction methods also exist that are, however, based on specific (special) k-space sampling trajectories. One example is the back-projection in radial MRT imaging. The latter cannot be used in the propeller technique according to the present state of the art.